# Index of Refraction Calculator

Created by Davide Borchia
Last updated: Aug 16, 2022

Light gets slowed and bent by the various materials met in its path: learn how with our index of refraction calculator.

In this short article, you will learn:

• What is the index of refraction;
• How to calculate the index of refraction;
• The index of refraction of water and glass (we didn't choose them randomly); and
• The relative index of refraction.

## What is the index of refraction

Translucent materials modify the behavior of light when crossed by it. If you thought that the speed of light is a universal constant, you are only partially correct. The speed of light is constant in a given medium, with the value $c$ being the one for a perfect vacuum.

What we call the "index of refraction" is, technically, the absolute index of refraction. This slight difference in naming states that we are not referencing the value to other indexes of refraction.

Light in a vacuum moves as fast as possible: the lack of interaction with matter allows photons to go as fast as possible. When light penetrates a material (glass, water, a solution, etc.), the electric fields interact, interfering with the propagation.

## How to calculate the index of refraction

To calculate the index of refraction, you must know the speed of light in the medium. Theoretically, you can calculate the refractive index ab initio, but a microscopic modelization of the material for the purpose is complex and — in most cases — pointless.

The equation for the index of refraction explicates the magnitude of this interference:

$n = \frac{c}{v}$

Where:

• $n$ is the index of refraction
• $c$ is the speed of light in the vacuum; and
• $v$ is the phase speed of light in the medium.

From this formula, we can see that the index of refraction of vacuum is $n=1$. Light travels in empty space unperturbed.

🙋 What is the phase speed of light? The phase speed of light is different from the speed of the particle and describes the speed of the phase of each component of a wave packet. The speed at which the packet moves is the group speed, and it is a distinct quantity. Only in the vacuum do the two quantities coincide. Not clear: look at this .

For most materials, the index of refraction for visible light is bigger than $1$, and usually less than 2.

Some materials are transparent at different frequencies (infrared, ultraviolet, radio frequencies, etc.) of the spectrum: salt is transparent to IR radiation, and some polymers allow UV light through without much interference. We can usually identify higher indexes of refraction, but surprisingly, also values of the index of refraction of light smaller than $1$. When this happens, the phase speed is higher than the group velocity $c$.

Wait: isn't $c$ the universe's ultimate speed limit? Yes! But only for physical objects. The phase of a wave is just a point in space; consequently, it can move faster than light. We didn't break the universe since this kind of object can transport no information.

## The effects of the index of refraction on light

Ok, lights slows down, so what? The first and foremost effect we can identify is a change in the propagation angle. This change is quantified by Snell's law.

The index of refraction is dependent on the wavelength. If you shine a ray of light composed of multiple wavelengths (read: colors), a passage in a material with a different refraction index would split the ray into monochromatic components. The famous prism experiment is an easy and sticking proof of this phenomenon.

As light slows down in a medium, other particles can travel faster than the speed limit. When this happens with a charged particle, a phenomenon similar to the sonic boom can be detected. The pressure waves — the noise of a supersonic object — are replaced by light with a characteristic blue hue: the Cherenkov radiation.

## Some examples: the index of refraction of glass and water

Look out of the window: those trees, or houses, are not in the right position! Even though the image looks undistorted (and thanks technology for this: a glass from a century ago would not be as flat and defectless!), the underlying physics tells us that the image is, in fact, in the wrong place!

The index of refraction of glass is, on average, $n = 1.52$. For those few millimeters, the light slows down, just to accelerate again.

Water is the other material we are most used to looking through. Either a pond, the sea, or a glass on your desk. In water, the index of refraction is lower than the one of glass, with $n = 1.333$. If you assumed the opposite, think for a second about the average thickness of glass you are looking through.

🙋 You can use the index of refraction calculator to calculate the speed of light with the index of refraction. Insert the desired value of the index of refraction: we will invert the formula for you!

## The relative index of refraction

Since in our daily experience, light travels in different mediums rather than vacuum, choosing the speed of light in the vacuum as a reference for the calculations of the index of refraction is not always convenient.

Physicists use the relative index of refraction of light to compare the refractive indexes and, as a consequence, the distortion of a light ray between two materials.

The relative index of refraction has equation:

$n_{21} = \frac{v_1}{v_2}$

Where $v_1$ and $v_2$ are the phase speed of light in the two media, notice how the value of the constant $c$ has been canceled from the equation.

Davide Borchia
Mode
Absolute index of refraction
Medium
Air
Speed in medium (v)
mi/s
Index of refraction
To calculate the angle of refraction, use our Snell's law calculator 🐌
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